In the letter pair series FI, KM, PQ, ?, which pair should replace the question mark to continue the pattern?

Introduction / Context:
The series FI, KM, PQ, ?, consists of pairs of letters where both letters move forward through the alphabet by fixed amounts. This is a classic, straightforward alphabet test question where we simply apply constant steps to both columns of letters to predict the next pair.

Given Data / Assumptions:

• Given pairs: FI, KM, PQ, ?
• Alphabet positions A 1 to Z 26.
• We treat first letters and second letters as two separate sequences.

Concept / Approach:
We analyse the sequence of first letters F, K, P, ? and the sequence of second letters I, M, Q, ?. Converting letters to numbers allows us to compute the differences between terms. Once we see that both sequences follow simple arithmetic progressions, we extend them by one term to find the missing pair.

Step-by-Step Solution:
Step 1: First letters are F, K, P. Step 2: Positions: F 6, K 11, P 16. Step 3: Differences are 11 minus 6 equals 5, and 16 minus 11 equals 5. So the first letters increase by 5. Step 4: Next first letter is 16 plus 5 equals 21, which is U. Step 5: Second letters are I, M, Q. Step 6: Positions: I 9, M 13, Q 17. Step 7: Differences are 13 minus 9 equals 4, and 17 minus 13 equals 4. So the second letters increase by 4. Step 8: Next second letter is 17 plus 4 equals 21, which is also U. Step 9: Therefore the missing pair is UU.

Verification / Alternative check:
Write all pairs numerically: FI 6,9; KM 11,13; PQ 16,17; UU 21,21. First letters: 6, 11, 16, 21 follow a plus 5 pattern, and second letters: 9, 13, 17, 21 follow a plus 4 pattern. Only UU in the options satisfies these progressions for both positions at the same time.

Why Other Options Are Wrong:
MO gives first letter M 13, which does not follow the plus 5 pattern from P 16. ZA has Z 26 and A 1, which would require wrap around and non constant steps. TO and TV change the first or second letter to positions that do not maintain plus 5 or plus 4 sequences from the previous terms. Thus they cannot be correct.

Common Pitfalls:
Some candidates search for a single fixed step for the entire pair instead of checking each letter separately. Others forget to compare both sequences and accept an option that only fits one of the columns. The reliable strategy is to convert letters to positions, compute the differences for each sequence, and demand that the chosen pair satisfies both progressions.

Final Answer:
The pair that correctly continues the series is UU.